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1、Chapter 3 Relativistic Quantum Mechanics,Introduction,Non-relativistic quantum mechanics relativistic quantum mechanics Schrdinger equation Klein-Gordon equation S integer Dirac equation S half integer Spin is automatically contained in Dirac equation,3.1 Klein Gordon equation,Lorentz transormation
2、time, space are of the same weight K G equation,3.1 Klein Gordon equation,3.1 Klein Gordon equation,3.1 Klein Gordon equation,3.1 Klein Gordon equation,Discussion Negative energy instable,3.1 Klein Gordon equation,Negative probability,3.1 Klein Gordon equation,3.1 Klein Gordon equation,Non-relativis
3、tic limit: K-G eq Sch eq,3.1 Klein Gordon equation,3.1 Klein Gordon equation,3.1 Klein Gordon equation,With electromagnetic field,3.1 Klein Gordon equation,3.1 Klein Gordon equation,Covariant form,3.1 Klein Gordon equation,3.1 Klein Gordon equation,3.1 Klein Gordon equation,3.2 Dirac equation,How to
4、 overcome the negative probability difficulty,3.2 Dirac equation,3.2 Dirac equation,3.2 Dirac equation,3.2 Dirac equation,The condition for and 1) They must follow the relation 2) Operator H must be Hermitian 3) Lorentz invariance,3.2 Dirac equation,3.2 Dirac equation,3.2 Dirac equation,3.2 Dirac eq
5、uation,4 anti-commute matrices and 44 matrices,3.2 Dirac equation,3.2 Dirac equation,Conservation law of the probability flux,3.2 Dirac equation,3.2 Dirac equation,3.3 solutions of the free particle,3.3 solutions of the free particle,3.3 solutions of the free particle,3.3 solutions of the free parti
6、cle,3.3 solutions of the free particle,3.3 solutions of the free particle,3.3 solutions of the free particle,3.3 solutions of the free particle,3.3 solutions of the free particle,Discussion Positive energy state (=+1) Negative energy state (=-1) Eigenstates of momentum p,3.3 solutions of the free pa
7、rticle,Orbital angular momentum is not conserved,3.3 solutions of the free particle,3.3 solutions of the free particle,Spin angular momentum,Or,3.3 solutions of the free particle,3.3 solutions of the free particle,3.3 solutions of the free particle,3.3 solutions of the free particle,Helicity operato
8、r,3.3 solutions of the free particle,3.3 solutions of the free particle,If ,we find,Eigenvalues:,3.3 solutions of the free particle,Eigenstates:,3.3 solutions of the free particle,3.3 solutions of the free particle,Dirac hole theory Dirac sea Hole: (+Ep0, +m0, +e0) (positron) 1932, Anderson discover
9、ed positron from cosmic ray using cloud chamber,3.4 Dirac equation in the central force field,Equation in non-relativistic limit,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,In non-relativistic approximation
10、,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,Noting: up to the order Normalization condition must be ensured,3.4 Dirac equation in the central force field,3.4 D
11、irac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,By using,3.4 Dirac equation in the central force field,Relativistic correction of kinetic energy,3.4 Dirac equation in th
12、e central force field,Thomas term,Darwin term,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,Quantum number K,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dir
13、ac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,Radial equations,3.4 Dirac equa
14、tion in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,3.4 Dirac equation in the central force field,We take,3.5 Solution of the Dirac equation in the Coulomb field,Motivation Discussion the Hydrogen atom Fine structure,3.5 Solutio
15、n of the Dirac equation in the Coulomb field,3.5 Solution of the Dirac equation in the Coulomb field,3.5 Solution of the Dirac equation in the Coulomb field,3.5 Solution of the Dirac equation in the Coulomb field,3.5 Solution of the Dirac equation in the Coulomb field,3.5 Solution of the Dirac equat
16、ion in the Coulomb field,n=0,1,2, , n=1,2,3,3.5 Solution of the Dirac equation in the Coulomb field,3.5 Solution of the Dirac equation in the Coulomb field,Ground state 1S1/2 (n=0, =-1, n=1, j=1/2),3.5 Solution of the Dirac equation in the Coulomb field,3.5 Solution of the Dirac equation in the Coul
17、omb field,3.5 Solution of the Dirac equation in the Coulomb field,Question Dirac eq + non-relativistic limit Sch eq Z137 ? No limit for Z Uniform charged sphere ? No limit for Z Fine structure Enj En for Sch eq,3.6 Klein paradox,Another question for the non-relativistic limit of Dirac equation Does
18、positron exist Scalarlike potential and vectorlike potential,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,At the infinity, the wave function is not zero, which means that there is only the scattering state solution instead of bound state solution,3.6 Klein paradox,3.6 Klein paradox,The phys
19、ics of Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,If p=mc,3.6 Klein paradox,T
20、he explanation of Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.6 Klein paradox,3.7 MIT bag model,Motivation: can we establish a model to confine quark scalarlike potential,3.7 MIT bag model,3.7 MIT bag m
21、odel,3.7 MIT bag model,Introducing scalarlike potential,3.7 MIT bag model,3.7 MIT bag model,3.7 MIT bag model,When gg we find a exponentially decaying solution,3.7 MIT bag model,Solution of step function,3.7 MIT bag model,3.7 MIT bag model,3.7 MIT bag model,3.7 MIT bag model,3.7 MIT bag model,3.7 MIT bag model,3.7 MIT bag model,